Shock propagation through a local constriction

Abstract

The interaction of a shock wave with a localized constriction in a straight conduit is investigated by systematically varying the blockage ratio in the range 0.35-0.75, the normalized constriction length in the range 0.25-2, and the incident Mach numbers of 1.4 and 1.8. Abrupt rectangular constrictions and smoothly contoured sinusoidal constrictions are considered, as they provide two limiting configurations. Validated Large-eddy simulations resolve both the transient start-up dynamics and the subsequent propagation of reflected and transmitted shock waves. The results show that, for rectangular constrictions, the reflected shock strength depends primarily on the blockage ratio and is largely independent of length, whereas the transmitted shock exhibits measurable sensitivity to constriction length. In contrast, sinusoidal constrictions display a strong coupling between blockage and length, with the reflection process governed by the local contour slope and evolving reflection topology. The start-up process within the constriction occurs over time scales one to two orders of magnitude longer than the shock passage time and is characterized by a sequence of reflection, separation, and flow reorganization events that determine the eventual steady shock configuration. At later times, the reflected shock Mach number scales linearly with blockage ratio, while the transmitted shock strength decreases monotonically with increasing blockage. Based on these trends, semi-empirical models are developed to predict the strengths of both reflected and transmitted shocks across the parameter space considered. These results provide a unified framework for understanding and predicting shock propagation in conduits with localized geometric variations, with direct relevance to compressible internal flows in engineering and natural systems.

Figures (13)

• Figure 1: Schematic figure of the problem, (a) represents the initial condition for a rectangular constriction and (b) represents the later state. (c,d) represents the same for a sinusoidal constriction.
• Figure 2: Schematics of the experimental system (a) The shock tube apparatus (b) the interchangeable constriction model installed in the test section, and (c) the optical setup used to perform high-speed schlieren imaging.
• Figure 3: A schematic description of shock wave interaction with a local constriction in a straight conduit. (a)-(d) depicts the interaction with a smooth sinusoidal local constriction. (e)-(h) depicts the interaction with a sharp rectangular local constriction. RS- reflected shock wave, TS - Transmitted shock wave, SS - standing shock wave
• Figure 4: Comparison of the LES results against experimental schlieren imaging and wall pressure measurements for two constriction geometries with ${h}=10mm$ (BR = 0.5) and $L$ = 40 mm ($\tilde{L}=1$).Panels (a,b) and (f,g) compare experimental schlieren images with numerical schlieren computed from density gradients at different times. Panels (c,d,e) and (h,i,j) compare LES and experimental wall pressure signals at three transducer locations: $x = -127.5\,\mathrm{mm}$ (upstream of the constriction), and $x = 42.5\,\mathrm{mm}$ and $x = 357.5\,\mathrm{mm}$ (downstream of the constriction). All pressure traces are shifted to $t = 0$ at the arrival of the incident shock at the most upstream transducer.
• Figure 5: The transient evolution of the shock-flow interaction within localized constrictions for cases with BR = 0.5, and different normalised lengths, $\tilde{L}=0.25,1$. For each case, line integral convolution (LIC) visualizations (top rows) illustrate the instantaneous flow structure, while the corresponding pressure fields (bottom rows) show the spatial pressure distribution.